Playing Cards Probability Questions

Playing Cards Probability questions are a helpful topic for students who want to understand maths in a easy way. Probability questions help us to find the probability of drawing a card from a pack of 52 cards. Playing Cards this topic is important as it creates a strong base in maths and improves problem solving skills. Students can practice different questions to see how Playing Cards Probability questions are used in real examples.

What is the Probability of Playing Cards?

Playing cards probability means finding a particular card or group of cards from a well shuffled standard deck.

P(Event) =  Number of favorable cards
                   ____________________________

                  Total cards in deck (= 52)

Standard Deck of 52 Playing Cards

STANDARD DECK:

Total cards = 52

Total suits = 4

Cards per suit = 13

Total face cards = 12

Total number cards = 36

Total aces = 4

Structure of a Deck of Playing Cards

4 SUITS IN A DECK:

♥ Hearts    → Red   → 13 cards

♦ Diamonds  → Red   → 13 cards

♣ Clubs     → Black → 13 cards

♠ Spades    → Black → 13 cards

Total = 4 × 13 = 52 cards

Face Cards

FACE CARDS (with human faces):

King (K)   → 4 cards (one per suit)

Queen (Q)  → 4 cards (one per suit)

Jack (J)   → 4 cards (one per suit)

Total face cards = 12

Number Cards

NUMBER CARDS (Ace through 10):

Ace (A) = 4 cards

    2       = 4 cards

    3       = 4 cards

    4       = 4 cards

    5       = 4 cards

    6       = 4 cards

    7       = 4 cards

    8       = 4 cards

    9       = 4 cards

   10      = 4 cards

Total number cards = 10 × 4 = 40

Red and Black Cards

RED CARDS:

♥ Hearts (13) + ♦ Diamonds (13) = 26 red cards

BLACK CARDS:

♣ Clubs (13) + ♠ Spades (13) = 26 black cards

Total = 26 + 26 = 52

Kings, Queens, Jacks and Aces

Card	Count	Red ones	Black ones
Ace	4	2 (♥,♦)	2 (♣,♠)
King	4	2 (♥,♦)	2 (♣,♠)
Queen	4	2 (♥,♦)	2 (♣,♠)
Jack	4	2 (♥,♦)	2 (♣,♠)

Playing Cards Probability Formula

Basic Probability Formula

P(E) = n(E) / n(S)

n(E) = number of favorable cards

n(S) = 52 (total cards in deck)

Range: 0 ≤ P(E) ≤ 1

Probability of Drawing One Card

One card drawn from well-shuffled deck:

n(S) = 52

P(specific card like Ace of Hearts) = 1/52

P(any Ace) = 4/52 = 1/13

P(any Heart) = 13/52 = 1/4

P(any face card) = 12/52 = 3/13

Types of Playing Cards Probability Questions

Complete Reference Table

Card Type	Count	Probability
Ace	4	4/52 = 1/13
King	4	4/52 = 1/13
Queen	4	4/52 = 1/13
Jack	4	4/52 = 1/13
Face Cards (King, Queen, Jack)	12	12/52 = 3/13
Number Cards (Ace–10)	40	40/52 = 10/13
Red Cards	26	26/52 = 1/2
Black Cards	26	26/52 = 1/2
Hearts (♥)	13	13/52 = 1/4
Diamonds (♦)	13	13/52 = 1/4
Clubs (♣)	13	13/52 = 1/4
Spades (♠)	13	13/52 = 1/4
Red Kings	2	2/52 = 1/26
Black Queens	2	2/52 = 1/26
Any Specific Card	1	1/52

Solved Examples on Playing Cards Probability

Q1: Find the probability of drawing a Queen.

Total Queens = 4

P(Queen) = 4/52 = 1/13

Answer: 1/13

Q2: Find P(red card).

Red cards = 26

P(red) = 26/52 = 1/2

Answer: 1/2

Q3: Find P(Heart).

Hearts = 13

P(Heart) = 13/52 = 1/4

Answer: 1/4

Q4: Find P(not an Ace).

Aces = 4

Not Ace = 52 - 4 = 48

P(not Ace) = 48/52 = 12/13

OR: P(not Ace) = 1 - P(Ace) = 1 - 1/13 = 12/13

Answer: 12/13

Q5: Find P(King or Queen).

Kings = 4

Queens = 4

King OR Queen = 8 (mutually exclusive)

P(King or Queen) = 8/52 = 2/13

Answer: 2/13

Q6: Find P(red face card).

Red face cards:

♥ King, ♥ Queen, ♥ Jack = 3

♦ King, ♦ Queen, ♦ Jack = 3

Total = 6

P(red face card) = 6/52 = 3/26

Answer: 3/26

Q7: Find P(black Ace).

Black Aces: Ace of Clubs, Ace of Spades = 2

P(black Ace) = 2/52 = 1/26

Answer: 1/26

Q8: Find P(number card that is red).

Red cards = 26 (13 Hearts + 13 Diamonds)

Red face cards = 6

Red number cards = 26 - 6 = 20

P(red number card) = 20/52 = 5/13

Answer: 5/13

Q9: Find P(Ace or black card).

Using inclusion-exclusion:

P(Ace or Black) = P(Ace) + P(Black) - P(Black Ace)

P(Ace) = 4/52

P(Black) = 26/52

P(Black Ace) = 2/52

P(Ace or Black) = 4/52 + 26/52 - 2/52

               = 28/52

               = 7/13

Answer: 7/13

Q10: Find P(face card or Spade).

Face cards = 12

Spades = 13

Face cards that are Spades = 3 (K♠, Q♠, J♠)

P(face or spade) = (12 + 13 - 3)/52

                 = 22/52

                 = 11/26

Answer: 11/26

Q11: Find P(neither face card nor Ace).

Face cards = 12

Aces = 4

Face cards OR Aces = 16

Neither = 52 - 16 = 36

P(neither) = 36/52 = 9/13

Answer: 9/13

Playing Cards Probability Questions with Answers

Q1: P(drawing a specific card, e.g., 7 of Hearts)?

Answer: 1/52

Q2: P(drawing any 7)?

7s in deck = 4

Answer: 4/52 = 1/13

Q3: P(drawing a card less than 5, counting Ace=1)?

Cards: A,2,3,4 in each suit = 4×4 = 16

Answer: 16/52 = 4/13

Q4: P(drawing a black Jack)?

Black Jacks = Jack of Clubs + Jack of Spades = 2

Answer: 2/52 = 1/26

Q5: P(drawing a Diamond King)?

Only 1 such card

Answer: 1/52

Q6: P(drawing a card that is both red and a King)?

Red Kings = King of Hearts + King of Diamonds = 2

Answer: 2/52 = 1/26

Q7: P(drawing a 10)?

Four 10s in deck

Answer: 4/52 = 1/13

Q8: P(not drawing a face card)?

Non-face = 52 - 12 = 40

Answer: 40/52 = 10/13

Q9: P(drawing a Club or a Heart)?

= 13 + 13 = 26

Answer: 26/52 = 1/2

Q10: P(drawing a red Queen or black King)?

Red Queens = 2

Black Kings = 2

Total = 4

Answer: 4/52 = 1/13

Q11: A card is drawn. Find P(card has a value more than 9). (Take Ace = 1)

Cards with value > 9:

10, Jack, Queen, King = 4 types × 4 suits = 16

P = 16/52 = 4/13

Answer: 4/13

Q12: Find P(card is a prime number card).

Prime numbers on cards: 2, 3, 5, 7

Each appears 4 times = 4 × 4 = 16

P(prime number) = 16/52 = 4/13

Answer: 4/13

Download PDF - Playing Cards Probability Questions

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